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Re: How much will my undergrad affect my chances at top 10?
I don’t see why you need to complete two master’s programs. Doing well (near the top of your class) in the EME should be sufficient to get admitted at least to LSE with funding, which is a top 10 school if you go by placements. I agree with ahududu that fretting about top 5 is pointless, and I have gotten the sense that seats in top 5 programs can be filled almost exclusively by people connected to “top 5 mills” like Opportunity Insights, Gentskow-Shapiro, or NBER (Harvard/MIT predocs). If you do a predoc at a top 10 school, your expected outcomes should be somewhere in the top 30; however, if I really did well in LSE EME I would simply take the LSE offer and roll with it! It’s about as good as it can get in that scenario.